Generalized Riccati Equation Mapping Method: 27 Solutions for Josephson Junctions and Nonlinear Optics Models

The generalized Riccati equation mapping method and Jumarie's Riemann-Liouville fractional derivative were utilized in order to acquire the 27 analytic solutions for the nonlinear space-time fractional (2+1)-dimensional cubic Klein-Gordon equation and the nonlinear space-time fractional (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation. Both of these equations are nonlinear as well. Of the many possible behavior solutions that were accessible for these nonlinear evolution equations, the kink and periodic wave behavior solutions were the ones that were available. Three-dimensional, two-dimensional, and contour forms of the behavior graphs were shown by us. Compared to a number of other methods, the generalized Riccati equation mapping method offers a greater variety of solutions to these equations. This technique displays the behavior of the solution as a wave in a number of different forms, which is shown by the results of this research.